Question

Which example correctly demonstrates polynomial addition?
A. (2x²+6x+1) + (3x²+3x+9) = 5x²+9x+10
B. (2x²+6x+1) + (3x²+3x+9) = 5x⁴+9x²+10
C. (2x²+6x+1) + (3x²+3x+9) = 13x²+9x+10
D. (2x²+6x+1) + (3x²+3x+9) = -x²+3x-8

Answer 1

To determine which example correctly demonstrates polynomial addition, we need to add the polynomials \( (2x^2 + 6x + 1) \) and \( (3x^2 + 3x + 9) \) together.

1. **Add the coefficients of \(x^2\)**:
- \(2 + 3 = 5\)

2. **Add the coefficients of \(x\)**:
- \(6 + 3 = 9\)

3. **Add the constant terms**:
- \(1 + 9 = 10\)

Putting it all together, we get:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

Now we can compare this result to the provided options:

A. \( (2x²+6x+1) + (3x²+3x+9) = 5x²+9x+10 \) ✔️ Correct
B. \( (2x²+6x+1) + (3x²+3x+9) = 5x⁴+9x²+10 \) ❌ Incorrect
C. \( (2x²+6x+1) + (3x²+3x+9) = 13x²+9x+10 \) ❌ Incorrect
D. \( (2x²+6x+1) + (3x²+3x+9) = -x²+3x-8 \) ❌ Incorrect

Thus, the correct answer is **A**.